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It seems the only reason I would close the card is if BoA rate-jacked your mother, in which case rejecting the change of terms and closing the account would keep the regular interest rate in-tact. However, short of affecting both you and your mother's scores, there is no way to just close the account and only pay principle. The interest rate applies to the balance you and/or your mother charged, and isn't canceled out just by closing the card.
For the sake of keeping your lines of credit, I would pay it off as fast as you can, adding even an extra dollar or two per month. Unless your interest rate was jacked from say 10% to 25%, in which case I would reject the terms and close the account, if I couldn't pay it off in a few months.